{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 绘制IMU轨迹的脚本"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "import os\n",
    "#表示当前所处的文件夹上一级文件夹的绝对路径\n",
    "filepath=os.path.abspath('..')+\"/result\"  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imu仿真得到的不加噪声的真值\n",
    "position = []\n",
    "quaterntions = []\n",
    "timestamp = []\n",
    "tx_index = 5\n",
    "\n",
    "with open(filepath + '/imu_true_value.txt', 'r') as f:\n",
    "    \n",
    "    data = f.readlines()     # txt中所有字符串读入data\n",
    "    for line in data:\n",
    "        odom = line.split()  # 将单个数据分隔开存好\n",
    "        numbers_float = list(map(float, odom))  # 转化为浮点数\n",
    "        position.append([numbers_float[tx_index], numbers_float[tx_index + 1], numbers_float[tx_index + 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imu真实值经过欧拉积分得到的轨迹\n",
    "position1 = []\n",
    "quaterntions1 = []\n",
    "timestamp1 = []\n",
    "with open(filepath + '/imu_true_euler.txt', 'r') as f: \n",
    "\n",
    "    data = f.readlines()  # txt中所有字符串读入data\n",
    "    for line in data:\n",
    "        odom = line.split()  # 将单个数据分隔开存好\n",
    "        numbers_float = list(map(float, odom))  # 转化为浮点数\n",
    "        position1.append([numbers_float[tx_index], numbers_float[tx_index + 1], numbers_float[tx_index + 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imu真实值经过中值积分得到的轨迹k\n",
    "position2 = []\n",
    "quaterntions2 = []\n",
    "timestamp2 = []\n",
    "with open(filepath + '/imu_true_median.txt', 'r') as f:  \n",
    "\n",
    "    data = f.readlines()  # txt中所有字符串读入data\n",
    "    for line in data:\n",
    "        odom = line.split()  # 将单个数据分隔开存好\n",
    "        numbers_float = list(map(float, odom))  # 转化为浮点数\n",
    "        position2.append([numbers_float[tx_index], numbers_float[tx_index + 1], numbers_float[tx_index + 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 带有噪声的IMU数据的欧拉积分\n",
    "position3 = []\n",
    "quaterntions3 = []\n",
    "timestamp3 = []\n",
    "with open(filepath + '/imu_noise_euler.txt', 'r') as f:  \n",
    "\n",
    "    data = f.readlines()  # txt中所有字符串读入data\n",
    "    for line in data:\n",
    "        odom = line.split()  # 将单个数据分隔开存好\n",
    "        numbers_float = list(map(float, odom))  # 转化为浮点数\n",
    "        position3.append([numbers_float[tx_index], numbers_float[tx_index + 1], numbers_float[tx_index + 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 带有噪声的IMU数据的中值积分\n",
    "position4 = []\n",
    "quaterntions4 = []\n",
    "timestamp4 = []\n",
    "with open(filepath + '/imu_noise_median.txt', 'r') as f:  \n",
    "\n",
    "    data = f.readlines()  # txt中所有字符串读入data\n",
    "    for line in data:\n",
    "        odom = line.split()  # 将单个数据分隔开存好\n",
    "        numbers_float = list(map(float, odom))  # 转化为浮点数\n",
    "        position4.append([numbers_float[tx_index], numbers_float[tx_index + 1], numbers_float[tx_index + 2]])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 计算误差，用向量的二范数衡量\n",
    "# 积分的时候初始位置没有保留，所以从[1:4000]\n",
    "e_eulur = np.array(position)[1:4000,:] - np.array(position1)\n",
    "norm_E_eulur = np.linalg.norm(e_eulur,axis=1,keepdims=True)\n",
    "# 中值积分的\n",
    "e_median = np.array(position)[1:4000,:] - np.array(position2)\n",
    "norm_E_median = np.linalg.norm(e_median,axis=1,keepdims=True)\n",
    "\n",
    "time = np.arange(1/200, 20,1/200)\n",
    "plt.plot(time,norm_E_eulur)\n",
    "plt.plot(time,norm_E_median)\n",
    "plt.xlabel('simulation time /s')\n",
    "plt.ylabel('Error /m')\n",
    "plt.legend(['Eulur','Median'])     #添加图例\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    " ### plot 3d\n",
    "\n",
    "#  precision_mid = np.linalg.norm(np(position4-position))\n",
    "#  precision_eulor = np.linalg.norm(np(position1-position))\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "\n",
    "xyz =  list(zip(*position))      #真值\n",
    "xyz1 = list(zip(*position1))     #真值欧拉积分　\n",
    "xyz2 = list(zip(*position2))     #真值中值积分\n",
    "xyz3= list(zip(*position3))      #加入噪声的欧拉积分\n",
    "xyz4= list(zip(*position4))      #加入噪声的中值积分\n",
    "print\n",
    "ax.plot(xyz[0], xyz[1], xyz[2], label='gt')\n",
    "ax.plot(xyz1[0], xyz1[1], xyz1[2], label='raw_eulur')\n",
    "ax.plot(xyz2[0], xyz2[1], xyz2[2], label='raw_median')\n",
    "ax.plot(xyz3[0], xyz3[1], xyz3[2], label='noise_eulur')\n",
    "ax.plot(xyz4[0], xyz4[1], xyz4[2], label='noise_median')\n",
    "ax.legend()\n",
    "\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:python36] *",
   "language": "python",
   "name": "conda-env-python36-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
